DLMF:35.7.E4 (Q9815)

From DRMF
Revision as of 14:57, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:35.7.E4
No description defined

    Statements

    Defining formula
    lim c → ∞ ⁡ F 1 2 ⁡ ( a , b c ; 𝐈 - c ⁢ 𝐓 - 1 ) = | 𝐓 | b ⁢ Ψ ⁡ ( b ; b - a + 1 2 ⁢ ( m + 1 ) ; 𝐓 ) . subscript → 𝑐 Gauss-hypergeometric-of-matrix-pFq 2 1 𝑎 𝑏 𝑐 𝐈 𝑐 superscript 𝐓 1 superscript 𝐓 𝑏 confluent-hypergeometric-of-matrix-Psi 𝑏 𝑏 𝑎 1 2 𝑚 1 𝐓 {\displaystyle{\displaystyle\lim_{c\to\infty}{{}_{2}F_{1}}\left({a,b\atop c};% \mathbf{I}-c\mathbf{T}^{-1}\right)=|\mathbf{T}|^{b}\Psi\left(b;b-a+\tfrac{1}{2% }(m+1);\mathbf{T}\right).}}
    0 references
    DLMF id
    DLMF:35.7.E4
    0 references
    Symbols used
    generalized hypergeometric function of matrix argument
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; 𝐓 ) Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝐓 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}
    xml-id
    C35.S8.E1.m2acdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q9815&oldid=52691"